The consumer price index (CPI) is a measure of the average change in prices over time in a fixed market basket of goods and services typically purchased by consumers. One of the items in this market basket that affects the CPI is the price of oil and its derivatives. The file titled Consumer contains the price of the derivatives of oil and the CPI adjusted to 2005 levels. In Problem 15-49, backward elimination stepwise regression was used to determine the relationship between CPI and two independent variables: the price of heating oil and of diesel fuel.
a. Construct an estimate of the regression equation using the same variables.
b. Produce the appropriate residual plots to determine if the linear function is the appropriate regression function for this data set.
c. Use a residual plot to determine if the residuals have a constant variance.
d. Produce the appropriate residual plot to determine if the residuals are independent. Assume the data were extracted in the order listed.
e. Construct a probability plot to determine if the error terms are normally distributed.